arXiv subjects

Katalin Friedl

Publications and source records attributed to Katalin Friedl.

8 recordsLinked to original sources

arXiv2026

Resident fitness computation in linear time and other algorithmic aspects of interacting trajectories

Systems of interacting trajectories were recently studied in~\cite{HGSTW24}. Such a system of $[0,1]$-valued piecewise linear trajectories arises as a scaling limit of the system of logarithmic subpopulation sizes in a population-genetic model (more precisely, a Moran model) with mutation and selection. By definition, the resident fitness is initially 0 and afterwards it increases by the ultimate slope of each trajectory that reaches height 1. We show that although the interaction of $n$ trajectories may yield $Ω(n^2)$ slope changes in total, the resident fitness function can be computed algorithmically in $O(n)$ time. Our algorithm uses the so-called continued lines representation of the system of interacting trajectories. In the special case of Poissonian interacting trajectories where the birth times of the trajectories form a Poisson process and the initial slopes are random and i.i.d., we provide a linear bound on the expected total number of slope changes.

cs.DS↗

arXiv2026

Succinct QUBO formulations for permutation problems by sorting networks

Quadratic Unconstrained Binary Optimization (QUBO) is a standard NP-hard optimization problem. Recently, it has gained renewed interest through quantum computing, as QUBOs directly reduce to the Ising model, on which quantum annealing devices are based. We introduce a QUBO formulation for permutations using compare-exchange networks, with only $O(n \log^2 n)$ binary variables. This is a substantial improvement over the standard permutation matrix encoding, which requires $n^2$ variables and has a much denser interaction graph. A central feature of our approach is uniformity: each permutation corresponds to a unique variable assignment, enabling unbiased sampling. Our construction also allows additional constraints, including fixed points and parity. Moreover, it provides a representation of permutations that supports the operations multiplication and inversion, and also makes it possible to check the order of a permutation. This can be used to uniformly generate permutations of a given order or, for example, permutations that commute with a specified permutation. To our knowledge, this is the first result linking oblivious compare-exchange networks with QUBO encodings. While similar functionality can be achieved using permutation matrices, our method yields QUBOs that are both smaller and sparser. We expect this method to be practically useful in areas where unbiased sampling of constrained permutations is important, including cryptography and combinatorial design.

quant-ph↗

arXiv2021

Quantum Inspired Adaptive Boosting

Building on the quantum ensemble based classifier algorithm of Schuld and Petruccione [arXiv:1704.02146v1], we devise equivalent classical algorithms which show that this quantum ensemble method does not have advantage over classical algorithms. Essentially, we simplify their algorithm until it is intuitive to come up with an equivalent classical version. One of the classical algorithms is extremely simple and runs in constant time for each input to be classified. We further develop the idea and, as the main contribution of the paper, we propose methods inspired by combining the quantum ensemble method with adaptive boosting. The algorithms were tested and found to be comparable to the AdaBoost algorithm on publicly available data sets.

quant-ph↗

arXiv2013

Some Improvements to Total Degree Tests

A low-degree test is a collection of simple, local rules for checking the proximity of an arbitrary function to a low-degree polynomial. Each rule depends on the function's values at a small number of places. If a function satisfies many rules then it is close to a low-degree polynomial. Low-degree tests play an important role in the development of probabilistically checkable proofs. In this paper we present two improvements to the efficiency of low-degree tests. Our first improvement concerns the smallest field size over which a low-degree test can work. We show how to test that a function is a degree $d$ polynomial over prime fields of size only $d+2$. Our second improvement shows a better efficiency of the low-degree test of Rubinfeld and Sudan (Proc. SODA 1992) than previously known. We show concrete applications of this improvement via the notion of "locally checkable codes". This improvement translates into better tradeoffs on the size versus probe complexity of probabilistically checkable proofs than previously known.

cs.CC↗

arXiv2013

When the largest eigenvalue of the modularity and normalized modularity matrix is zero

In July 2012, at the Conference on Applications of Graph Spectra in Computer Science, Barcelona, D. Stevanovic posed the following open problem: which graphs have the zero as the largest eigenvalue of their modularity matrix? The conjecture was that only the complete and complete multipartite graphs. They indeed have this property, but are they the only ones? In this paper, we will give an affirmative answer to this question and prove a bit more: both the modularity and the normalized modularity matrix of a graph is negative semidefinite if and only if the graph is complete or complete multipartite.

math.SP↗

arXiv2008

Singular value decomposition of large random matrices (for two-way classification of microarrays)

Asymptotic behavior of the singular value decomposition (SVD) of blown up matrices and normalized blown up contingency tables exposed to Wigner-noise is investigated.It is proved that such an m\times n matrix almost surely has a constant number of large singular values (of order \sqrt{mn}), while the rest of the singular values are of order \sqrt{m+n} as m,n\to\infty. Concentration results of Alon et al. for the eigenvalues of large symmetric random matrices are adapted to the rectangular case, and on this basis, almost sure results for the singular values as well as for the corresponding isotropic subspaces are proved. An algorithm, applicable to two-way classification of microarrays, is also given that finds the underlying block structure.

math.PR↗

arXiv2005

On the black-box complexity of Sperner's Lemma

We present several results on the complexity of various forms of Sperner's Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is linear in the separation number of the skeleton graph of the manifold and the size of its boundary. As a corollary we get an $O(\sqrt{n})$ deterministic query algorithm for the black-box version of the problem {\bf 2D-SPERNER}, a well studied member of Papadimitriou's complexity class PPAD. This upper bound matches the $Ω(\sqrt{n})$ deterministic lower bound of Crescenzi and Silvestri. The tightness of this bound was not known before. In another result we prove for the same problem an $Ω(\sqrt[4]{n})$ lower bound for its probabilistic, and an $Ω(\sqrt[8]{n})$ lower bound for its quantum query complexity, showing that all these measures are polynomially related.

quant-ph↗

arXiv2002

Quantum testers for hidden group properties

We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of two functions having identical ranges within each coset of some normal subgroup. Our periodicity tester is efficient in Abelian groups and generalizes, in several aspects, previous periodicity testers. This is achieved by introducing a technique refining the majority correction process widely used for proving robustness of algebraic properties. The periodicity tester in non-Abelian groups and the common coset range tester are query efficient.

quant-ph↗